# Sig Turbulence / Flow over Periodic Hills

Olivier Brugiere, Universite Joseph Fourier, Grenoble, France

## 1 Motivation

Figure 1 : Periodic hill

The flow over bodies with massive separation constitutes an important area of applications for LES. In many geometrie we can find this kind of flow like the 2D backward-facing step, the asymmetric diffuser or the periodic hill. We know experimental's data which was made by Almeida et al. [1] but in Mellen and al. [2] et Temmerman et al. [3] we can find that they have an influence of the side wall so the 1995 ERCOFTAC/IAHR workshop have cast a doubt on the true periodicity of the experimental configuration. But we have some data from LES with a good mesh like [[1]]. Flow over 2D periodic is in fact an experimental configuration with 9 hills. For the computational, we represent this configuration by a channel periodic with two half's hills like on the figure 1.

The probleme of this flow is the separtion bubble which is due to a adverse pressure gradient that's why this is a test case for many subgrid scale models (SGS) and for near-wall low.

## 2 Testcase description

### 2.1 Flow configuration

#### 2.1.1 Geometrical Parameters

• Hill's heigh : $h = 28 mm$
• Streamwise distance : $L_{x} = 9,0 h$
• Normal wall heigh  : $L_{y} = 3,035 h$
• Spanwise distance  : $L_{y} = 4,5 h$

#### 2.1.2 Boundary condition

• Streamwise condition : periodicity
• Spanwise condition : periodicity
• Normal to streamwise : two walls

### 2.2 Simulation details

Figure 2 : Hill mesh

We have make the geometry on Gambit Fig 2 and the mesh is composed by $Nx \times Ny \times Nz = 118 \times 33 \times96$.

The aim of my study is testing a posteriori near-wall low. To compare we are running three cases :

• With near-wall low
• With the Spalding Low [4]
• With the Mahart et al. low [5]

## 3 Numerical results

Results of the simulations are available in the paper written by Duprat et al. [6]

## 4 References

[1] Almeida, Durao and Heitor, 1993, Experimental thermal and fluid science, Vol. 7, pp. 87-101.

[2] Mellen, Frohlich and Rodi, 2000, Large Eddy Simulation of the flow over periodic hills, 16th IMACS World Congress , Lausanne. [2]

[3] Temmerman and Leschziner, 2001, Large Eddy Simulation of separated flow in a streamwise periodic channel construction, Int. Symp. on Turbulence and Shear Flow Phenomena, Stockholm, June 27-29. [3]

[4] Spalding, 1961, A single formula for the law of the wall, Jl. Appl. Mech., vol 28, pp. 455-457

[5] Manhart, Peller and Brun, 2008, Near-wall scaling for turbulent boundary layers with adverse pressure gradient, Theor. Comput. Fluid Dyn., vol 22 , pp. 243-260.

[6] Duprat, Balarac, Métais, Congedo, and Brugière, O., 2011, A wall-layer model for large-eddy simulations of turbulent flows with/out pressure gradient. Physics of Fluids, 23, 015101.[4]

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